where \(f_1, \mathcal {E}_{\omega } \propto E_\omega \)  and \(f_2, \mathcal {E}_{2\omega } \propto E_{\omega }^2\)  in the lowest order in the incident field amplitude. Note, that \(f(\mathbf {p}, x, t)\)  [as well as \(\mathcal {E}_x(x,t)\) ] also contains time-independent non-equilibrium corrections \(\propto E_{\omega }^2\) .
These corrections determine static edge polarization and dc edge currents [1]}, [2]}. However, they are not relevant for SHG and are omitted.
